In parallelogram ABCD, the height, lowered to the side of CD, divides it in two and forms an angle of 30

univerkov | March 28, 2021 | education

In parallelogram ABCD, the height, lowered to the side of CD, divides it in two and forms an angle of 30, AB = 12 cm with the side BC. Find the perimeter.

In a parallelogram, opposite sides are equal, therefore AB = CD, AD = BC.

By condition, the height ВH divides the side of the CD in half, then CH = HD = CD / 2 = 12/2 = 6 cm.

Consider a right-angled triangle ВСН, in which the angle СН, by condition, is equal to 30, therefore, the leg СН lies opposite the angle 30 and is equal to half of the hypotenuse ВС. Then BC = 2 * CH = 2 * 6 = 12 cm.

Determine the perimeter of the parallelogram.

P = AB + BC + CD + AD = 12 + 12 + 12 + 12 = 48 cm.

Answer: P = 48 cm.

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